/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Find the slope and the \(y\) -in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 33

Find the slope and the \(y\) -intercept of each line whose equation is given. $$9 x-8 y=0$$

Short Answer

Expert verified
The slope is \(\frac{9}{8}\) and the y-intercept is 0.

Step by step solution

01

Rewrite the Equation

Rewrite the given equation in standard form as follows: \[9x - 8y = 0\]
02

Isolate the y-term

To find the slope and y-intercept, we need to rewrite the equation in slope-intercept form \(y = mx + b\). Isolate the \(y\)-term: \[-8y = -9x\]
03

Solve for y

Divide both sides by -8 to solve for y: \[y = \frac{9}{8}x\]
04

Identify the Slope and y-intercept

In the equation \(y = \frac{9}{8}x\), the coefficient of \(x\) represents the slope (\(m\)) and the constant term represents the y-intercept (\(b\)). Here, the slope is \(\frac{9}{8}\) and the y-intercept is \(0\) since there is no constant term.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Linear Equations
Linear equations are mathematical expressions that create a straight line when graphed. They are called 'linear' because they graph as straight lines. A linear equation in two variables has the general form: \[Ax + By = C\], where A, B, and C are constants.
  • A: Coefficient of x
  • B: Coefficient of y
  • C: Constant term
The solutions to a linear equation are the coordinates (x, y) that lie on the line described by the equation. Understanding this fundamental concept is crucial when working with more complex algebraic functions. Linear equations are also utilized in various applications like economics, physics, and statistics.
Slope-Intercept Form
The slope-intercept form of a linear equation is \[y = mx + b\], where:
  • m: Slope of the line
  • b: y-intercept
The slope (m) represents the rate of change or the steepness of the line. It is calculated as the ratio of the vertical change to the horizontal change between two points on the line: \[m = \frac{(y_2 - y_1)}{(x_2 - x_1)}\] The y-intercept (b) is the point where the line crosses the y-axis. For instance, in the provided solution, the slope (\[m = \frac{9}{8}\]) tells us how slanted the line is, and the y-intercept (\[0\]) tells us that the line passes through the origin (0,0).
Standard Form
The standard form of a linear equation is given as \[Ax + By = C\]. It is another way to express linear equations, different from the slope-intercept form. Here,
  • \[A\]: The coefficient of \[x\]
  • \[B\]: The coefficient of \[y\]
  • \[C\]: A constant term
To convert an equation from standard form to slope-intercept form, you need to solve for \[y\]. For example, taking the equation given in the exercise: \[9x - 8y = 0\], we isolate the \[y\]-term to convert it:
  • Subtract \[9x\] from both sides: \[-8y = -9x\]
  • Divide by \[-8\]: \[y = \frac{9}{8}x\]
Now, it is in slope-intercept form \[y = mx + b\]. Understanding these forms makes it easier to graph and analyze linear equations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

To prepare for Section \(3.7,\) review solving a formula for \(a\) variable and subtracting real numbers (Sections 1.6 and 2.3 ). Simplify. $$8-(-5)$$

Pressure at Sea Depth. The function \(P(d)=1+(d / 33)\) gives the pressure, in atmospheres (atm), at a depth of \(d\) feet in the sea. Note that \(P(0)=1\) atm \(, P(33)=2\) atm, and so on. Find the pressure at 20 ft, at 30 ft, and at 100 ft.

Find the function values. $$f(n)=5 n^{2}+4 n$$ a) \(f(0)\) b) \(f(-1)\) c) \(f(3)\) d) \(f(t)\) e) \(f(2 a)\) f) \(2 \cdot f(a)\)

A Boeing 737 climbs from sea level to a cruising altitude of \(31,500\) ft at a rate of \(6300 \mathrm{ft} / \mathrm{min}\). After cruising for 3 min, the jet is forced to land, descending at a rate of \(3500 \mathrm{ft} / \mathrm{min} .\) Represent the flight with a graph in which altitude is measured on the vertical axis and time on the horizontal axis.

Why is slope-intercept form more useful than point-slope form when using a graphing calculator? How can point-slope form be modified so that it is more easily used with graphing calculators?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.